The proposed research project is aimed at a comprehensive study of the kinematic and dynamic characteristics of physiological pulsatile flow in curved arteries. A new computational method is formulated in this proposal to simulate the complete cycle of flow pulsation in distensible and rigid vessels. The flows in rigid tubes will serve as a special case in this project. The feasibility and effectiveness of the research endeavor are based on the new concept and formulation of the Navier-Stokes equations developed in this proposal. Otherwise, it would be "premature or extremely difficult" to tackle such a complicated, but significant, problem at this time. The main features of the three-dimensional time-dependent flow processes will be disclosed from the results of the oscillations of velocity field, pressure and viscous stresses, the interaction between the boundary layer (i.e., strong viscous effects near the vessel wall) and the irrotational core, and the transfer of momentum and energy in the unsteady spiral flow processes. The dynamic effects of distensibility of the wall on the shearing stresses distributions on the wall will be studied for different flow accelerations and decelerations. The input data for the computational flow simulatios will be taken from the temporal variations of pressure drops measured from an in-vitro model. The flow patterns (in-vitro) on three parallel planes will be photographed to compare with the calculated results. While the capability of computer is growing, it is timely to advance our computational techniques for unsteady three-dimensional flow problems. In particular, it has been thought and believed that the detailed hemodynamic information will be useful for the long-term research endeavors in genesis of atherosclerosis and deformity of arteries in various sites of the circulatory system. It is hoped and anticipated that the success of the proposed study will lead to better computational models (which will include the effects of branching flows and non-uniform cross-sections) in hemodynamic research with in-vivo experiments.